I have a 1/4" I.D. steel pipe with air flowing through it for glass chip removal. I need help in determining the velocity so I can calculate air usage.
The velocity will be determined by the pressure drop through the lenght of pipe, and whatever fittings & valves are installed. The outlet pressure will be atmospheric, and the inlet pressure will be whatever it is, in your plant system.
You can get an approximate (and limiting) flow rate by just treating the pipe as an orifice off the main line and applying Bernouli's equation. Upstream, figure your line pressure and zero (IE, negligible) velocity; at the orifice, figure zero (gauge) pressure and solve for velocity. Velocity times the area of the orifice would give you a flow rate for air at atmospheric pressure; correct if required to get the compressed volumetric flow rate. Actual flow could be 1/2 of this rate or less, depending on the conditions.
At the very end of the pipe, velocity will approach sonic condition. Choked flow will prevail, and the polytropic flow equation will geve a pretty good idea of the maximum oor "ideal" flow.
The actual condition will be somewhat less because you do not have a "clean" orifice, that is the flow will have the chance to develop in the immediately upstream portion of the pipe and thus there will be a velocity profile immediately upstream of the outlet, the portions nearest the pipe wall travelling slower than sonic...The density in this portion is also varying, so that analysis is more involved, but it can be solved as a function of length based on the assumption of constant entropy using ideal gas equation.
If the length of the 1/4" pipe is more than a few diameters, the result from the choked orifice equation will be significantly higher than actual.
This is probably the only portion of the pipe assembly you will need to analyze...Unless the upstream components are of similar size, its doubtful they will have any significant effect on the choke condition; they will represent a minor percentage of the total available pressure difference.
Do you know your source pressure and temperature? And outlet pressure? If Z is approx 1, then approximate the air as ideal gas with constant sp. heats.
Find the equivalent fL/d of piping. If flow can be considered as adiabatic, use the Fanno line to determine pipe entrance or exit conditions and hence flow. Check to see that choking does not occur in fittings or pipe between entrance or exit. If choking does occur, readjust your assumptions and use fanno line to point where choking occurs.
